Question: Jessica is 24 years younger than Daniel. For the last 3 years, Daniel and Jessica have been going to the same school. Four years ago, Daniel was 5 times older than Jessica. How old is Daniel now?
Solution: We can use the given information to write down two equations that describe the ages of Daniel and Jessica. Let Daniel's current age be $d$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $d = j + 24$ Four years ago, Daniel was $d - 4$ years old, and Jessica was $j - 4$ years old. The information in the second sentence can be expressed in the following equation: $d - 4 = 5(j - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to solve our first equation for $j$ and substitute it into our second equation. Solving our first equation for $j$ , we get: $j = d - 24$ . Substituting this into our second equation, we get the equation: $d - 4 = 5($ $(d - 24)$ $ -$ $ 4)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $d - 4 = 5d - 140$ Solving for $d$ , we get: $4 d = 136$ $d = 34$.